Compound Thick Lens: Calculating Refractive Power with Thick Lens Equation

[bowlbase]

Homework Statement

I have a compound thick lens problem that I need to find the sign of the refractive power.

Homework Equations

Thick lens equation and focal length equation.

The Attempt at a Solution

I believe all I need to do is calculate the focal length of the first two thick lenses and then use that result as the first "lens" in the same focal length equation again:

$\frac{1}{f_{12}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{d_{12}}{f_{1}f_{2}}$
$\frac{1}{f_{123}}=\frac{1}{f_{12}}+\frac{1}{f_{3}}-\frac{d_{123}}{f_{12}f_{3}}$

Is this a correct (or correct enough approximation) to get the sign?

 

[andrevdh]

Maybe you could "send in" parallel rays (object at infinity) and try and work out if the image formed by the system is real (+ sign) or virtual (- sign)? What information about the system is available?

 

[bowlbase]

Maybe you could "send in" parallel rays (object at infinity) and try and work out if the image formed by the system is real (+ sign) or virtual (- sign)? What information about the system is available?

I have all the dimensions of the lenses and distances between in the system.

 

[andrevdh]

HyperPhysics have decent summary of the relevant theory - Gullstrand's equation and principal planes.

 

[bowlbase]

What 'd' should be used for calculating the power when including the third lens? So I have the first two lenses easy enough. But I'm not sure if I take the P₁₂ to be the distance of the second lens, the average of the distance from 1->3 and 1->2 or just the total distance. I suspect it is the distance from the second lens but I"m not 100% sure.

 

[andrevdh]

Maybe you should treat each lens separately, otherwise you run into the problem you are now facing - how to locate the second principal plane, which in this instance seems to be "impossible"? Sorry not my forte.

 

[bowlbase]

Yeah, its been several years since I've had any optics classes so I'm struggling to remember. I recall doing some matrix multiplication for compound lenses but I don't dare delve that deeply. I don't think it is impossible, just more effort.

 

[andrevdh]

Scroll down to the Lensmaker's equation: http://www.newport.com/Optics-Formulas/144956/1033/content.aspx
What you can do then is propagate the object through the system of lenses to see whether they form a real or virtual image.